quick derivative question

**mathlete** · February 25th 2008, 03:34 PM

how would you differentiate

x^pi

and

x^(pi)^2 + (pi^2)^x

thanks...

**topsquark** · February 25th 2008, 04:59 PM

Originally Posted by mathlete

how would you differentiate

x^pi

and

x^(pi)^2 + (pi^2)^x

thanks...

The first one is easy:
$\frac{d}{dx} \left ( x^{\pi} \right ) = \pi x^{\pi - 1}$

The second is a bit harder, and I need you to clarify something: The first term is $\left ( x ^{\pi} \right ) ^2$ or $x^{\pi ^2}$ ?

The derivative of the second term is "simple." The formula is somewhat ugly, but there is one:
$\frac{d}{dx} \left ( a^x \right ) = ln(a) \cdot a^x$ .

-Dan

**mathlete** · February 25th 2008, 06:26 PM

the first term in the second part is x to the pi^2

**mathlete** · February 25th 2008, 06:38 PM

Originally Posted by topsquark

The first one is easy:
$\frac{d}{dx} \left ( x^{\pi} \right ) = \pi x^{\pi - 1}$

The second is a bit harder, and I need you to clarify something: The first term is $\left ( x ^{\pi} \right ) ^2$ or $x^{\pi ^2}$ ?

The derivative of the second term is "simple." The formula is somewhat ugly, but there is one:
$\frac{d}{dx} \left ( a^x \right ) = ln(a) \cdot a^x$ .

-Dan

thanks...i figured it out

for the first term i just used the power rule and got

pi^2x^(pi^(2)-1)+ln(pi^2)(pi^2)^x

and that was right...so thanks again

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